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Draw a directed graph for the relation R on the set {0, 1, 2, 3) given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.

Draw a directed graph for the relation R on the set {0, 1, 2, 3) given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Draw a directed graph for the relation \( R \) on the set \(\{0, 1, 2, 3\}\) given by: \[ R = \{ (0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3) \} \] **Explanation:** The directed graph (or digraph) of a relation involves creating vertices for each element in the set and drawing directed edges (arrows) according to the ordered pairs in the relation. **Vertices:** - The set of vertices is \{0, 1, 2, 3\}. **Edges:** - There is a directed edge from 0 to 1, since \((0, 1) \in R\). - There is a directed edge from 0 to 2, since \((0, 2) \in R\). - There is a directed edge from 1 to 2, since \((1, 2) \in R\). - There is a loop at 2, since \((2, 2) \in R\). - There is a directed edge from 3 to 1, since \((3, 1) \in R\). - There is a loop at 3, since \((3, 3) \in R\). **Graph Characteristics:** - Each vertex corresponds to an element in the set \{0, 1, 2, 3\}. - The edges are directed, indicating the relationship direction between elements. - Loops at a vertex indicate a relation from an element to itself. Visualizing this will help understand how these elements are related to each other within the set.
Transcribed Image Text:**Problem Statement:** Draw a directed graph for the relation \( R \) on the set \(\{0, 1, 2, 3\}\) given by: \[ R = \{ (0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3) \} \] **Explanation:** The directed graph (or digraph) of a relation involves creating vertices for each element in the set and drawing directed edges (arrows) according to the ordered pairs in the relation. **Vertices:** - The set of vertices is \{0, 1, 2, 3\}. **Edges:** - There is a directed edge from 0 to 1, since \((0, 1) \in R\). - There is a directed edge from 0 to 2, since \((0, 2) \in R\). - There is a directed edge from 1 to 2, since \((1, 2) \in R\). - There is a loop at 2, since \((2, 2) \in R\). - There is a directed edge from 3 to 1, since \((3, 1) \in R\). - There is a loop at 3, since \((3, 3) \in R\). **Graph Characteristics:** - Each vertex corresponds to an element in the set \{0, 1, 2, 3\}. - The edges are directed, indicating the relationship direction between elements. - Loops at a vertex indicate a relation from an element to itself. Visualizing this will help understand how these elements are related to each other within the set.
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